INTRODUCTION AND MOTIVATION
Literature review
5G and beyond-5G networks will support diverse use cases and significantly enhance mobile data capacity, the number of connected devices, and user data rates compared to existing mobile systems Moreover, integrating context and location information is expected to enhance both traditional and innovative technologies, helping to tackle various challenges within these advanced networks.
The majority of 5G devices will benefit from enhanced location awareness due to advancements in global navigation satellite systems (GNSS), which are being introduced alongside the existing global positioning system (GPS) These systems, combined with ground support and multiband operations, aim to achieve location accuracies of approximately 1 meter in open areas In environments where GNSS signals are weak or absent, such as urban canyons or indoors, alternative local radio technologies like ultrawideband (UWB), Bluetooth, ZigBee, and radio frequency identification (RFID) will enhance Wi-Fi-based positioning, enabling submeter accuracy.
Accurate location information enhances network performance across all layers of the communication protocol stack At higher layers, it facilitates natural applications like location-aware information delivery and traffic-related services In contrast, lower layers, including PHY, MAC, network, and transport layers, utilize a channel quality metric (CQM) to correlate channel performance indicators with user positions By predicting user location at time t, channel qualities at the new position can be estimated, allowing for adjustments in system parameters such as power and modulation type to optimize channel conditions.
This section explores various research applications related to channel quality mapping, focusing on CQM and predictive engines It begins with an examination of location-aware mmWave beamforming, a critical aspect of 5G technology, which presents unique challenges Next, it discusses vehicular communication, emphasizing the exchange of sensor data, a key component in the development of fully autonomous vehicles envisioned in 5G and beyond Finally, it reviews prior studies on the location-awareness of wireless communication.
1.1.1 Location-awareness in mmWave beamforming
The Multiple-Input Multiple-Output (MIMO) system offers significant benefits through beamsteering and beamforming, essential for mitigating channel attenuation in mmWave signals The small wavelength characteristic of this frequency band enables the dense arrangement of multiple antenna elements, enhancing the effectiveness of their combined radiation patterns.
The potential benefits of beamforming are challenging to harness due to the complexities involved in the discovery process, especially in systems utilizing a single RF front per side The inherent one-look limitation of analog beamforming necessitates that both the base station and user equipment direct their antenna beams in varying directions to achieve a successful antenna lock-on.
Digital beamforming provides enhanced flexibility in directional cell search techniques, allowing users to access digital samples from all antenna elements However, the increased number of required RF front ends can lead to high costs, making it impractical for user equipment.
Analog beamforming, despite its limitation of a single directional focus, presents benefits such as lower costs, reduced complexity, and minimized power consumption due to its use of a single RF front-end Consequently, there is a growing interest in employing analog beamforming in millimeter-wave (mmW) wireless systems, either as a standalone solution or in conjunction with digital precoding in hybrid configurations.
An innovative approach leverages site-specific propagation characteristics to enhance communication systems By creating a database linked to user equipment locations, which is informed by extensive measurements across the area, it enables the simulation of channels through ray-tracing techniques This predictive modeling allows for determining the optimal orientation of both the base station and user equipment, ultimately improving performance and connectivity.
In a study utilizing a ray-tracing tool, both direct and reflected rays, as well as scattered rays, are simulated to enhance understanding of mmWave channels The authors introduce a simplified beamforming scheme that focuses antennas on a few dominant paths, as mmWave channels exhibit less complexity compared to traditional radio signal channels, characterized by a Line-Of-Sight (LOS) or quasi-LOS with limited dominant path clusters and lower multipath components This approach allows for simultaneous steering of beams toward the four strongest paths, leveraging the inherent space diversity of the multipath channel Additionally, in scenarios involving sudden channel disruptions, such as human blockage, the system can quickly adjust by accessing a stored database to realign beams with alternative non-blocked dominant paths.
A low-complexity beamforming technique for moving vehicles, particularly trains, is introduced, utilizing location information to enhance performance By assuming the train follows a fixed track, the search space is effectively reduced Pre-stored beamforming weights are matched with the train's location data at the base station, eliminating the need for channel tracking or energy detection This approach leads to significant improvements in bit-error rates and successful handover probabilities.
Location information can effectively enhance communication by directing beams toward dominant multipath links Additionally, simulations using ray-tracing can create a database of signal power at different locations, allowing for the calculation of beamforming weights and the selection of optimal beam pairs.
1.1.2 Location-awareness in vehicular communications
The number of sensors on vehicles, and the rate of data that they generate, is in- creasing Nowadays, there are around 60 - 100 sensors on a vehicle on average [14].
There could be about 200 sensors per vehicle for luxury cars [14] At present, automo- tive radars and visual cameras are the most common safety sensors found in vehicles.
Automotive radars enhance vehicle safety and functionality by detecting the presence, position, and speed of surrounding vehicles and objects, enabling features like adaptive cruise control, blind spot detection, lane change assistance, and parking assistance Meanwhile, cameras improve driving conditions by eliminating blind spots, acting as virtual mirrors, and enhancing night vision through infrared sensors Additionally, the advancement of autonomous vehicles heavily depends on LIDAR technology, which utilizes lasers to create high-resolution depth maps, generating data volumes comparable to traditional automotive cameras and significantly increasing the overall data output of vehicles.
A significant challenge faced by many sensor technologies is their limited sensing range To overcome this, wireless communications can be utilized, allowing vehicles to exchange information and form what is known as a connected vehicle system This connectivity offers two main advantages: first, by selecting an appropriate carrier frequency, vehicles can communicate even in non-line-of-sight situations, such as around corners; second, with a high bandwidth communication link, vehicles can share raw sensor data at accelerated rates This data sharing enables the implementation of adaptive platooning and the potential for cloud-driven, fully automated driving.
Dedicated Short-Range Communication (DSRC) is the advanced protocol designed for vehicle connectivity, enabling effective vehicle-to-vehicle (V2V), vehicle-to-infrastructure (V2I), and vehicle-to-everything (V2X) communication systems.
Challenges and motivations
To adapt to new environments at different locations, it is essential to create a database that maps channel qualities to specific locations This process involves making modifications in the lower layers, such as the PHY, MAC, network, and transport layers.
The current construction techniques are either for narrowband signal [24] or based on ray-tracing simulation [19, 20], or via assuming a fixed, simple path-loss model
The ray-tracing and ray-launching methods are complex and require detailed environmental information, making them less adaptable to changes such as new obstacles or human presence Additionally, while angles of arrival (AOAs), angles of departure (AODs), and delays are considered, the amplitudes of individual multipath links remain underexplored In contrast, some current localization techniques treat ultra-wideband (UWB) channels as multiple resolved multipath components (MPCs) Recent developments include algorithms for tracking and mapping these individual MPCs using commercial UWB RF devices Consequently, constructing a multipath-based database focused on millimeter-wave or wideband signals is anticipated to provide a more flexible, simpler, and autonomous approach to managing obstacles.
To achieve the anticipated levels of positioning accuracy, it is essential to tackle several critical signal processing challenges that enable seamless and widespread localization These challenges encompass the integration and fusion of various positioning technologies, managing errors arising from difficult propagation environments and interference, and simplifying systems through decentralization to enhance overall efficiency.
Purposes and objectives
This dissertation aims to explore the potential of utilizing location information to enhance wireless network performance It proposes a novel propagation model designed to predict Channel Quality Metrics (CQMs) for individual Multi-Path Components (MPCs) at new locations, leveraging a database of measured data Additionally, an algorithm will be introduced to demonstrate the effectiveness of incorporating location information into wireless network optimization.
This dissertation focuses on indoor wireless communication networks utilizing mmWave or UWB signals The current research will be conducted in an obstacle-free environment, but there is potential for future studies to explore scenarios involving obstacles or human interference.
Research hypotheses
1.4.1 Towards a site-specific radio propagation modeling
In 5G and beyond-5G systems, the increasing signal bandwidth allows for the resolution of multipath signals Due to high path loss attenuation in mmWave signals, only a few dominant multipath components (MPCs) are anticipated in the channel These resolvable MPCs are valuable for applications like beamforming and vehicular communications By knowing the locations of the transmitter and receiver, along with environmental details such as obstacle locations, site-specific MPCs can be effectively deduced.
Research hypothesis 1 is defined as:
Hypothesis 1: In a sparse multipath channel (mmWave or UWB signals), prop- agation model for individual multipath links can be built to ease the process of learn- ing/predicting of these MPCs.
1.4.2 Towards a large-scale predicting of radio channel statistics
Signaling overhead poses a significant challenge in Machine-to-Machine (M2M) communications and the Internet of Things (IoT), often leading to bottlenecks despite the integration of location awareness Additionally, the selection of Channel Quality Metrics (CQM) is crucial, as more accurate data can enhance performance but may also increase complexity, reduce robustness, and elevate overhead.
Hypothesis 2: Large scale channel statistics of various system performance indi- cators can be predicted in a simple way which help alleviating the signaling overhead problems.
1.4.3 Towards a side information-aided single-anchor multipath- based localization
Over the past two decades, numerous localization algorithms have emerged, with popular techniques including received signal strength (RSS), continuous wave radar, and ultra-wideband (UWB) methods While the RSS-based method often struggles with issues like multipath fading and shadowing, leading to reduced accuracy, the latter two techniques typically necessitate advanced hardware This dissertation introduces the use of channel quality metrics (CQM) as supplementary information to enhance localization accuracy with a commercial UWB transceiver, forming the basis of Research Hypothesis 3.
Hypothesis 3: For localization algorithms, CQM is expected to improve the al- gorithm robustness and accuracy in challenging environments with dense multipath or obstacles.
This thesis enhances location-aware applications in communication systems by introducing a site-specific propagation model capable of predicting large-scale channel statistics, including SINR, position error bound (PEB), and specular multipath component amplitudes (SMCs) These indicators are essential for optimizing mmWave beamforming lock-on times and improving scheduling in ultra-reliable low-latency communication (URLLC) scenarios Additionally, the research demonstrates the effectiveness of incorporating redundant information, specifically channel quality metrics (CQM), into a single-anchor localization system to bolster its robustness against blockages and obstacles.
This thesis is structured into seven chapters, beginning with an introduction in Chapter 1 that outlines the motivation, contributions, and framework of the study Chapter 2 presents the system and signal models, detailing the formulation of key channel parameters and performance indicators In Chapter 3, the Gaussian Process Regression (GPR) is introduced as an inference engine, utilizing the propagation model to predict channel statistics across the entire floor plan Chapter 4 provides visual data and discussions regarding the prediction of the Radio Environment Map (REM) Finally, Chapter 5 formulates a localization algorithm that incorporates REM as supplementary information.
Localization results are also shown Chapter 6 concludes the thesis Measurement campaigns together with mathematical derivations are shown in the appendices.
SIGNAL AND SYSTEM MODELS
Introduction
In localization systems, the accuracy is significantly influenced by channel conditions, particularly by the presence of multipath components (MPCs) Unlike communication systems where transmitted data is independent of the channel, localization relies on channel parameters like Time of Arrival (TOA) and Received Signal Strength (RSS) to convey positional information Consequently, there is a critical need for channel models that effectively capture the relationship between position and channel properties for location-aware applications.
Classical narrowband empirical statistical models, such as Hata-like models, primarily focus on the average path loss in relation to radial distance, incorporating multipath effects solely through statistical fading descriptions These models are empirical in nature and require calibration measurements for proper parameterization.
Empirical-statistical propagation models focus on capturing the temporal characteristics of multipath signals, including both specular and diffuse components, across various environments These models utilize a parametric tapped-delay-line approach, making them effective for characterizing Time of Arrival (TOA) measurements and their associated uncertainties in Ultra-Wideband (UWB) localization applications.
Deterministic Ray Tracing and Ray Launching models utilize Geometrical Optics to effectively characterize the specular component of a specific environment To achieve accurate results, it is essential to have a well-defined input database that details the environment, including terminal positions and system configuration.
Ray-tracing calculation methodologies have been around for decades, yet their widespread use has been limited The primary challenge has historically been the extensive computation time required to determine the propagation paths from the map, making this task particularly time-consuming.
To overcome this bottleneck intelligent methods have been implemented Furthermore,
HW acceleration has been also utilized These advances have made already the speed to be on an acceptable level.
The landscape of mobile radio systems is evolving with the introduction of modern wideband, high-speed technologies that utilize MIMO beamforming and advanced transmission techniques Performance is increasingly influenced not only by signal-to-noise ratio (SNR) but also by the complex characteristics of radio channels Ray Tracing models are emerging as effective tools for precise, site-specific field predictions and for multidimensional analysis of radio propagation across time, space, and polarization Recent advancements have led to the development of extensions that address diffuse scattering phenomena, capturing signals scattered in various directions due to the irregularities of surfaces and building structures Additionally, a non-stationary Gaussian model has been implemented to effectively represent the diffuse multipath component (DMC).
In this dissertation, we are interested in a hybrid geometric/stochastic channel model with several advantages First of all, it is less complex compared to Ray-tracing.
The model discussed in this chapter is designed to function without prior environmental information and can adapt to changes such as blockages Section 2.2 introduces the system model, highlighting the significance of the Virtual Anchor (VA) concept Additionally, Section 2.3 presents the relevant formulas for the system's signal.
System model
2.2.1 Representation of reflectors using virtual anchors (VAs)
Virtual anchors (VAs) are the key concept that is used VAs are well established in the literature to model specular reflections in wireless transmissions, be it acoustic
This section focuses on the computation and determination of VAs in a closed room environment, although the system discussed in this thesis is applicable beyond indoor settings.
Electromagnetic waves emitted from a transmit antenna in a closed room travel to a receive antenna under far-field conditions In this scenario, plane waves serve as a solution to the wave equation, with uniqueness achieved through boundary conditions defined by the reflective properties of the walls By solving the wave equation with these boundary conditions, one can derive the multipath-channel impulse response between the transmitter and receiver, similar to the approach used for acoustic waves To satisfy the boundary conditions for electromagnetic waves on walls, a virtual source model can effectively describe the wave behavior at the wall surfaces.
A-priori known reflectors/environment - Exact Virtual Anchor (VA) position
In this case, VA positions are computed with exact floor plan, i.e., room geometry, knowledge By mirroring the j-th anchor w.r.t walls, first-order VAs are constructed.
Higher-order VAs are computed by mirroring VAs w.r.t walls [49] and [47].
Figure 2.1: Illustration of multipath geometry using VAs for transmission between a PA and a mobile agent with exact floor plan information, as seen in [50, Fig 1].
Figure 2.2: Illustration of the VAs for the PA and an agent with PDF p(VA) and p(agent) , respectively, as seen in [51, Figure 1.1] The VA false represents a false detection of VA
Figure 2.1 presents a geometric model depicting the signal exchange between a physical anchor (PA) and an agent The black lines represent specular reflections occurring at the room walls, which can be accurately modeled using virtual anchors (VAs).
1, VA 2, VA 3 that are mirror-images of the j-th anchor w.r.t walls [26, 47].
A-priori known reflectors/environment with uncertainties - Prob- abilistic VA positions
To address uncertainties in the floor plan, the deterministic geometric model of the VA positions is transformed into a probabilistic model This is illustrated in Figure 2.2, where the joint probability density function (PDF) p(agent, PA, VA1, VA2, VA3) represents the positions of the agent and VAs If the position of the PA is considered known with certainty, the joint PDF simplifies to p(agent, VA1, VA2, VA3).
Figure 2.2 presents a probabilistic geometric environment model, illustrating the joint probability density function (PDF) of the agent and virtual anchor (VA) positions as a multivariate Gaussian random variable (RV) The marginal distributions are depicted with dashed black ellipses for the agent and red ellipses for the VA positions Notably, the marginal distribution p(a_false) indicates a misidentified VA at the position a_false While the anchor position a(j)_1 is assumed to be accurately known, the uncertainty in the floor plan implies that VA positions are also uncertain, represented by RVs Furthermore, this uncertainty suggests that the floor plan information may be incorrect, inconsistent, or completely absent, necessitating that positioning and tracking algorithms utilizing VAs account for this lack of knowledge.
2.2.2 Floor plan/environment information for location-aware ap- plications
For location-aware applications, we assumed that every RF device has the capability to provide location of its own or via cooperating with other devices.
In indoor environments, floor plans can be effectively represented by Virtual Anchors (VAs), whose positions may be precisely determined using the multipath-assisted indoor navigation and tracking (MINT) algorithm or estimated probabilistically through the Simultaneous Localization and Mapping (SLAM) algorithm This representation is advantageous as it allows for the absence of floor plan information; the SLAM algorithm simultaneously estimates both the agent's and the VAs' positions.
Hybrid geometric/stochastic signal model
In this study, we explore indoor environments where fixed anchors communicate with a mobile agent via radio signals As depicted in Figure 2.3, the j-th fixed anchor is represented as a blue cross at position \( a^{(j)}_1 \), while the agent is located at position \( p_l \) along a segmented trajectory Additionally, various virtual anchors (VAs) up to the second order are illustrated Throughout the thesis, fixed anchors are denoted by the index \( j \), spatial positions by \( l \), and the index \( k \) is utilized for deterministic Model Predictive Controllers (MPCs), with \( k=1 \) indicating the line-of-sight (LOS) component of the respective anchor.
VAs are mirror images of the PA at reflective surfaces, establishing a geometric model of specular multipath components (SMCs) originating from these surfaces The
VA model can therefore be used as a deterministic description of the delay, AOA, and AOD of these SMCs, given the position of the agent.
We describe the radio channel from the PA located at position a1 and the agent node located at positionpvia a geometry-based stochastic channel model (GSCM) by: h(t;p l ) K (j)
X k=1 α k (p l )δ(t−τ k (p l )) +ν(t;p l ), (2.1) where K (j) is the number of deterministic MPCs that correspond to the j-th anchor.
The first term on the right-hand side of equation (2.1) represents the sum of K(j) SMCs, characterized by amplitude α_k and delay τ_k, which are functions of the mobile agent's position p_l The delay τ_k(p_l) is determined by the distance between the agent and the respective points of interest, specifically the PA for k = 1 and the VA for k = 2 to K(j) This relationship is mathematically expressed as τ_k(p_l) = ∥p_l - a_k∥ / c, where a_k denotes the position of the relevant point.
− 5 0 5 10 15 20 x [m] y [m] segment 1 segment 2 segment 3 segment 4 segment 5 segment 6 segment 7 phys anchor VA a 4 a 8 a 10 a 13 a 17 a 2 a 1 a 6 a 11 a 19 a 7 a 3 a 12 a 16
The floor plan of the evaluation scenario is illustrated in Figure 2.3, where bold black lines represent walls, thick gray lines indicate glass windows, and other lines depict different materials The layout features a blue cross symbolizing physical anchors and orange circles representing virtual anchors (VAs) used in the experimental validation An agent navigates a trajectory divided into seven segments, each marked with unique colors The model incorporates the speed of light and accounts for diffuse multipath (DM) ν(t), which is represented as a zero-mean Gaussian random process.
We assume uncorrelated scattering along the delay axis, hence the autocorrelation function (ACF) ofν(t)is given by:
Kν(τ, u;p l ) =E{ν(τ;p l )ν ∗ (u;p l )}=Sν(τ;p l )δ(tưu), (2.2) whereSν(t;p l ) is the power delay profile (PDP) of the DM at agent position p l The
DM process is assumed to be quasi-stationary in the spatial domain, i.e S ν (τ;p l )does not change in the vicinity ofp l [53].
A baseband signals(t)is transmitted at carrier frequencyfc The complex envelope of the received signal then reads r(t;p l ) K (j)
The equation X k=1 α k (p l )s(t−τ k (p l )) + (s∗ν)(t;p l ) +w(t) illustrates the superposition of K (j) SMCs, where the first term represents this superposition, the second term involves the convolution of s(t) with the DMC ν(τ;p l ), and the third term accounts for measurement noise w(t), modeled as additive white Gaussian noise (AWGN) with a two-sided power spectral density of N 0 To reduce inter-symbol interference, root raised cosine (RRC) pulses are utilized for the transmitted signal, maintaining a pulse width Ts, while ensuring that the energy of s(t) is normalized to one.
Channel quality indicators
For UWB transmission, it is reasonable to assume that the SMC signals s k (t) s(t−τ k (p)) are well separated in delay domain and thus approximately orthogonal.
The SMC amplitude can be estimated by projecting the received signal onto the cor- responding shifted pulse [54], i.e. ˆ α k (p) Z T 0 r(t;p)s ∗ k (t)dt (2.4)
The variance of the estimated amplitude as derived in Appendix B is given as var[ ˆα k (p)] =E ν k (p) +w k | 2
The effective pulse duration is represented by the integral ∞|S(f)| 4 df The right-hand side consists of a Gaussian process related to the DMC and measurement noise Consequently, the estimated amplitude follows the distribution ˆ α k (p)∼ CN(α k (p), Sν(τ k ;p)Tp+N0).
The mean SMC amplitudes, denoted as α k (p), are deterministically influenced by the agent's position, p Additionally, the variance of these SMC amplitudes is affected by the interfering DM, which is characterized by the PDPS ν(τ k; p), as outlined in equation (2.2).
2.4.2 Signal-to-interference-plus-noise ratio (SINR)
Signal-to-Noise-and-Interference ratio (SINR) of the k-th MPC is defined as:
The SINR measures the ratio of energy from deterministic multipath components (MPCs) to the cumulative impact of additive white Gaussian noise (AWGN) and distortion metrics (DM) This ratio is crucial for assessing the position-related information contained in each MPC, which is essential for calculating the statistical performance bounds for multipath-assisted positioning, specifically the positioning error bound (PEB) discussed later in this chapter.
In [54], SINR of the k-th MPC is estimated via using the first and second order of the energy sample |α k (p l )| 2 which are denoted as mˆ 1,k and mˆ 2,k As detailed in
[54, 49], it is found based on a Ricean model of |αk(pl)|:
This moment-based estimator, as demonstrated in [49, eq (18)], is akin to traditional techniques used for estimating the Ricean K-factor in narrowband channels [55, 56] The approach has been adapted to assess local K-factors of deterministic multipath components (MPCs) in the delay domain.
Asymptotic variance analysis indicates that moment-based estimates of the K-factor demonstrate satisfactory performance, making them a compelling choice due to their lower computational demands compared to more complex methods like expectation-maximization approximations of maximum likelihood estimation.
The SINR estimates can be related to ranging uncertainties w.r.t the VAs using (3.14) This is used in [49] to tune the measurement noise model of a tracking filter.
1 For a block-spectrum signal the effective pulse duration is T p = R ∞
The equation −∞ |S(f)| 4 df = T s represents the Nyquist sampling time (T s) In contrast, for waveforms such as root-raised-cosine and raised-cosine, which exhibit a rectangular spectrum with tapered ends, the pulse duration (T p) is typically shorter than the Nyquist sampling time (T s) under standard symmetry conditions, as detailed in Appendix B.
Without loss of generality, we consider an isolated symbold from a linear alphabet (such as PAM or QAM) with E
|d| 2 = 1 that is transmitted at energy E s , using pulse waveform s(t) 2 The received waveform is thus y(t) =p
Assuming channel knowledge at the receiver, a matched filter can be used with impulse response (h∗s) ∗ (−t)/∥(h∗s)(t)∥ to obtain the decision variable z=p
E s d∥(h∗s)(t)∥+w, (2.11) wherewis now a zero-mean complex Gaussian variable with varianceN0 The Gaussian channel (2.11) has capacity
The analysis of channel impulse response h(t) reveals its significant influence on the system's performance, measured in bits per channel This relationship is further illustrated through the convolution of h(t) with the pulse shape s(t), which highlights the effect of signal bandwidth For clarity, we simplify the expression ∥(h∗s)(t)∥² to ∥eh∥², where the vector eh represents a sampled version of the filtered impulse response.
Ts(h∗s)(iTs) (2.13) obtained at rate 1/T s
To describe the contribution of one deterministic MPC to C0, the receiver samples the waveformy(t)with a filter matched to thek-th deterministic MPC s(t−τ k )(with
E s dh k +w (2.14) corresponding to a Gaussian channel with capacity
Following our channel model from (2.1), the channel gain h k is a Gaussian random variable itself, hk * K X k ′ =1 αk ′ s(t−τk ′ ) + (ν∗s)(t), s(t−τk)
A coded OFDM transmission system can effectively mitigate inter-symbol interference (ISI) in time-dispersive channels, approaching the theoretical capacity outlined in this study This analysis assumes that individual multipath components (MPCs) are orthogonal, allowing for their perfect separation by a wideband receiver Consequently, the channel response h_k is modeled as a complex normal distribution with mean α_k and variance linked to the power delay profile (PDP) of the multipath delay τ_k and the effective pulse duration T_p In a line-of-sight (LOS) scenario, the first component represents the LOS path, while subsequent components correspond to reflected paths.
Contribution of all deterministic MPCs
Assuming that the receiver can sample at all instances at which theK MPCs arrive.
The system can then be seen as a single-input-multiple-output (SIMO) channel Its model is
Under the assumption of orthogonality of the MPCs, the noise vectorw will consist of i.i.d complex Gaussian samples with varianceN 0 each This channel has capacity [62]
Furthermore, we will have ∥he∥ 2 > ∥h∥ 2 >|h k | 2 ,∀k, and consequentially C 0 > C all >
C k If MPCs overlap, i.e the orthogonality condition is violated, we may get∥h∥ 2 >
∥eh∥ 2 i.e C all > C 0 according to the definitions of this section.
To ensure an average Signal-to-Noise Ratio (SNR) at the receiver equal to N E s 0, it is essential to normalize the channel gains This normalization process involves analyzing an ensemble of Channel Impulse Responses (CIRs) while considering the effects of transmit pulse filtering The normalization is accomplished by multiplying the measured CIRs by a factor of 3.
To implement normalization effectively with a restricted set of data points, the expectation must be substituted with an arithmetic mean For convenience, we will denote this as E ℓ {x l } = L 1 P L.
ℓ=1 x ℓ ≈ E {X} for the average of a set of L samples x ℓ of random variable X.
The estimated MPC amplitudes α k , SINR-values SINR k , and PDP Sν(τ) yield predictions for the statistics ofeh,h k andhand thus for the capacitiesC 0 ,C k andC all The elements of ehare defined by
The statistics ofh k have been defined in (2.16) Forh, one needs to consider a channel vectorhas in (2.17) with components following (2.16).
It is in general not possible to give closed-form solutions for the PDFs resulting for
∥eh∥ 2 and∥h∥ 2 A Gaussian approximation is obtained for a “lumped gain” h¯ ∼ CN
The quadratic sum of the MPC amplitudes and the total DM powers is represented by equation (2.20) To approximate the squared magnitude of h¯, we use the relation |¯h| 2 ≈ ∥h∥ 2 This approximation indicates that the variability of |h¯| 2 serves as an upper limit on the variability of ∥h∥ 2, as it disregards the geometric aspects of the random components.
When analyzing the overall channel, it is essential to consider the dimensions of the DM process that may not align with the discrete MPCs An approximation can be achieved by defining a channel gain, where the real part reflects the quadratic sum of the MPC amplitudes with a variance similar to that of the real part of equation (2.20) Meanwhile, the imaginary part is characterized by a mean of zero and a variance that corresponds to the total DM power, subtracting the power of the real component, resulting in eh∼ N.
The approximation is again obtained as|eh| 2 ≈ ∥eh∥ 2 , representing also an upper bound for the true variability.
The channel model referenced in studies [49, 52, 63, 50] has been instrumental in analyzing multipath-assisted indoor positioning systems and developing related algorithms Specifically, in works [63, 50], the Position Error Bound (PEB) is derived for the signal model, highlighting how the delay information from each SMC enhances the effectiveness of positioning algorithms This thesis aims to conceptualize the PEB as a spatial field tailored to the current application environment, serving as an indicator of achievable positioning accuracy To establish this "environment model," a detailed explanation of the PEB will be provided.
The Positioning Error Bound (PEB) for multipath-assisted positioning is determined by the Cramer-Rao Lower Bound (CRLB), which quantifies the position error This is calculated as the square root of the trace of the upper left 2 by 2 submatrix of the inverse Fisher Information Matrix (FIM).
In the bistatic setup, the parameter vector ψ p T Rα T Iα T T includes the unknown location of the mobile agent and the complex amplitudes of the SMCs, which are considered nuisance parameters requiring estimation The equivalent Fisher Information Matrix (EFIM) is denoted as J p.
Chapter conclusions
This chapter outlines the system and signal models, detailing three key performance indicators: the Signal-to-Interference-plus-Noise Ratio (SINR) of the k-th Single-Mode Channel (SMC), the channel capacities for individual Multi-Point Channels (MPCs) as well as the collective capacities for all MPCs, and the Position Error Bound (PEB).
GAUSSIAN PROCESS REGRESSION FOR SMC AMPLITUDES 28 3.1 Related Work
SMC propagation model
The kth SMC is defined by a delay τ k (p) and a complex amplitude α k (p), with the delay modeled deterministically based on the agent's varying position p Specifically, τ k (p) is calculated as τ k (p) = 1/c ∥a k − p∥ = 1/c d k (p), where c represents the propagation speed The complex amplitude α k (p) is expressed as α k (p) = A(ϕ k (p))Γ k (ϕ k (p)) d k (p) exp.
The equation j2πfc 1 cd k (p) (3.1) represents the relationship between antenna gains of the transmitting (TX) and receiving (RX) antennas, along with the path loss at a reference distance of d0 = 1 m The antenna gains are determined by the direction angle ϕ k (p) =∠(p−a k ), which is defined by the line connecting the agent's position p and the virtual antenna's position a k Additionally, 1 Γ k (ϕ k (p)) indicates the reflection coefficient of the flat surface associated with the virtual antenna a k.
In the Line-of-Sight (LOS) component, we establish the coefficient Γ 1 (ϕ 1 (p)) without considering reflection Equation (3.1) can be broken down into two factors: a distance-dependent factor and an angle-dependent factor The distance-dependent factor includes the path-loss of a reflected SMC in free space along with a phase shift that varies with distance Meanwhile, the angle-dependent factor accounts for the agent and PA antenna patterns, represented as A(ϕ k (p)), and how the reflection coefficient Γ k (ϕ k (p)) changes with the incident angle This analysis assumes that the agent's position is a critical element in the overall system performance.
In this study, we assume that antenna gains remain nearly constant across the observed frequency range and that the antennas are non-dispersive When the physical anchor (PA) and the agent antennas are positioned at the same height with fixed orientations during measurements, the incident angle at the reflecting surface, along with the angles at both the agent and anchor used for calculating antenna gains, can be consolidated into a single angle, represented as ϕ k (p) = ∠(p−a k ) Consequently, the equation (3.1) can be reformulated as α k (p) = γ k (ϕ k (p)) d k (p) exp.
The equation j2πf c 1 c d k (p) illustrates the combined angle-dependence of antenna patterns and the reflection coefficient, represented as γ k (ϕ k (p)) = |γ k (ϕ k (p))|exp j∠γ k (ϕ k (p)) In the context of the diffuse component, we employ a complex Gaussian process, assuming uncorrelated scattering, which allows us to describe ν(τ;p) using the auto-correlation function outlined in 2.2 This approach effectively models the Power Delay Profile (PDP) Sν(τ;p) for the diffuse multipath (DM) scenario.
GP Modeling (GPM) of the SMC Amplitudes
The analysis in section 3.2 reveals that α k (p) exhibits a clear dependence on distance, while its angle dependence is influenced by various complex factors, such as antenna radiation patterns and building material reflection coefficients To effectively model the angle-dependent component of α k (p), we propose utilizing a Gaussian Process Regression (GPR) model, denoted as γ k (ϕ k (p)) GPR serves as a powerful regression tool for analyzing and predicting data, typically under the assumption of normal distribution This assumption is flexible, as large datasets often approximate a Gaussian distribution Additionally, our findings indicate that the data adheres to a (complex) Gaussian distribution, as evidenced in equation (2.7).
We refrain from applying the GPR model directly to complex amplitudes due to the challenges in achieving phase coherence of SMCs, especially when training data is recorded at uncertain positions Instead, we decompose complex amplitudes into real-valued absolute values and phase values The absolute values are Rician distributed, characterized by the Rician K-factor, where for K >> 1, the Rician distribution can be approximated by a Gaussian distribution Consequently, the GPR model is utilized to model the functions of absolute values and phase, represented as ψ(ϕ k (p)) and ζ(ϕ k (p)), with noise components for amplitude and phase, denoted as n abs ν,k and n ph ν,k, respectively, each having their own variance.
GPR
GPR usually consists of two steps: analyzing data obtained from measurements and predicting data at other positions that have not been measured.
Our goal is to model the angle-dependent SMC amplitude ψ(ϕ k (p)) and phase ζ(ϕ k (p)) using a Gaussian process model For the amplitude we have ψ(ϕ k (p))∼ GP à GP (ϕ k (p)), c GP (ϕ k (p), ϕ k (p ′ ))
, (3.5) whereà GP (ϕ k (p)): R 2 →R denotes the mean function and c GP (ϕ k (p), ϕ k (p ′ )): R 2 ì
The covariance function, also known as the kernel, is a crucial element in Gaussian Process Regression (GPR) It quantifies the similarities between observations at various data points, as illustrated by the relationship expressed in Eq (3.5) for the phase ζ(ϕ k (p)).
Covariance functions are typically defined by parameters, which, along with the mean function and noise, are collectively referred to as 'hyperparameters.' This section will provide a detailed description of these hyperparameters.
In this work, the mean value is modeled by the constant, i.e., à GP (ϕ k (p)) =m abs k (3.6)
(and m ph k for the phase) A squared exponential kernel is used for the covariance, c GP (ϕ k (p), ϕ k (p ′ )) =σ abs k 2 exp
The equation presented defines the covariance value as a function of agent positions (p, p′), where the correlation kernel's standard deviation (σ k abs) and characteristic correlation angle (a abs k) are key parameters Additionally, the standard deviation related to DMC (σ ν,k abs) is considered, alongside similar parameters for phase (σ k ph, a ph k, and σ ν,k ph) This mapping from R² × R² to R highlights the relationship between agent positions and their corresponding covariance.
The GP modeling of SMC amplitudes is grounded in specific models that, alongside data, uncover angle-dependent functions ψ(ϕ k (p)) and ζ(ϕ k (p)), as well as a variance linked to the DMC S ν (τ k ;p) The comprehensive hyper-parameter vectors necessary for the GP model, derived from the amplitude and phase data of SMC k, are represented as θ abs k = [a abs k , σ abs k , σ ν,k abs , m abs k ] T and θ k ph = [a ph k , σ k ph , σ ν,k ph , m ph k ] T.
The notation used in the term reflects the mapping of p ∈ R² to ϕₖ(p) ∈ R Additionally, the Dirac function δ(p − p′) signifies that the DMC are considered to be spatially uncorrelated.
In this section, we examine the fundamental principle of Generalized Polynomial Regression (GPR) For each specific model configuration (SMC) k, we establish a training dataset D k consisting of measurements y k,i = ψ(ϕ k (p i )) + ϵ, where i ranges from 1 to N These measurements are collected at training positions Ω = {p1, p2, , pN}, which are associated with angles ϕk = [ϕ k (p 1), , ϕ k (p N)] Additionally, ϵ is characterized as a normally distributed noise term, ϵ ∼ N(0, σ ϵ²), with variance σ ϵ² that correlates with the power spectral density of the Additive White Gaussian Noise (AWGN).
The training data is represented as a vector, yk = [y k,1, , y k,N] T Once the hyper-parameters are established, we can predict the mean and variance at the test position p ∗ with the angle ϕ k (p ∗ ) The mean and variance of the angle-dependent amplitude ψ(ϕ k (p ∗ )) or phase ζ(ϕ k (p ∗ )) can be expressed in closed form based on the data Dk and parameters θ abs k or θ ph k.
The variance of the predicted output, denoted as V[ψ(ϕ k(p ∗ ))|Dk,θ abs k ], is expressed as σ² k + σ abs ν,k² - k(ϕk(p ∗ ),ϕk)ᵀ K(ϕk)⁻¹ k(ϕk(p ∗ ),ϕk) Here, k(ϕk(p ∗ ),ϕk) represents the covariance vector of the Gaussian process, while à(ϕk) contains the mean values from the Gaussian process for the input data points The covariance matrix K(ϕk) incorporates the covariance function along with a noise term characterized by σ² ϵ and the Kronecker delta function A detailed analysis of the connection between the predicted variance, the probability density function (PDF) of the discrete memory channel (DMC), and the power spectral density of additive white Gaussian noise (AWGN) is provided in Appendix C.
In the GP prediction outlined in section 3.4.2, it is assumed that the hyper-parameter vector θ k abs (or θ k ph) is known However, if θ abs k is unknown, it must be estimated from the training database D k ={ϕk,yk} for each SMC The joint probability density function of the observed measurements yk, conditioned on the training angles ϕk, follows a Gaussian distribution, with both mean and covariance influenced by the hyper-parameter vector θ k abs This relationship is explicitly represented as à θ abs k and K θ abs k To estimate the parameter vector θ abs k (or θ k ph), the log-likelihood function is maximized, resulting in θˆ abs k = arg max θ k abs logp(yk|ϕk,θ k abs).
2(yk−à θ abs k (ϕk)) T K θ abs k (ϕk) −1 (yk−à θ abs k (ϕk))−N
Maximum likelihood estimation typically cannot be achieved in closed form, necessitating the use of numerical approximation methods Given the potential non-convex nature of the function, a global search is required to determine the parameters θˆ k abs (or θˆ k ph) across the domains of a abs k, σ abs k, and σ ν,k abs (or a ph k, σ k ph, and σ ν,k ph).
3.4.4 Evaluate the quality of prediction
Given a prediction method, we can evaluate the quality of prediction in several ways.
The squared error loss is one of the simplest loss functions; however, it is sensitive to the scale of the target values To address this issue, normalizing by the variance of the target values in the test cases leads to the standard mean squared error (SMSE).
In the context of GPR applied to absolute values of SMC amplitudes, we generate a predictive distribution for each test input, allowing us to assess the negative log probability of the target within the model To achieve meaningful insights, this loss must be standardized and averaged, resulting in the mean standard log loss (MSLL) [80].
To assess the quality of the model, the dataset will be split into two subsets: one for training and one for testing In addition to the training data, denoted as D k, the testing data set will also be established.
The dataset Dk is defined as {ϕ ∗ k , y ∗ k}, consisting of N ∗ measurements y k,i ∗ taken at specific positions p ∗ i The squared mean square error (SMSE) of the predicted mean E[ψ(ϕ k (p ∗ i))|D k ,θ abs k] is evaluated in relation to the angle-dependent amplitude ψ(ϕ k (p ∗ i)) or phase ζ(ϕ k (p ∗ i)) This evaluation is based on the learned parameters θ abs k or θ ph k, as outlined in equation (3.10).
In equation (3.14), \( y¯ ∗ k,i \) represents the average of the measurements, calculated as \( 1/N ∗ PN ∗ i=1y k,i \) The numerator reflects the sum of squared errors between the measured test data \( y k ∗ \) and the predicted mean, while the denominator captures the sum of squared errors between the measured test data \( y k ∗ \) and the average measurement \( y¯ ∗ k,i \) A significantly lower SMSE indicates superior prediction quality.
Experiment and result
In measurement campaign 2, data is collected from two physical anchors located at known positions, a(1)1 and a(2)1, which receive UWB signals from a mobile agent moving along a segmented trajectory Initially, all positions are unknown, and dipole coin antennas are utilized for this purpose.
The experimental setup utilizes antennas with a radiation pattern resembling isotropic characteristics in the horizontal plane, all mounted on a tripod at a uniform height to focus on 2-D propagation analysis All RF devices are linked to the Ilmsens UWB M-sequence sounder for calibration, as detailed in Appendix A.2 The Channel Impulse Response (CIR) obtained will undergo processing in the subsequent section, with further details provided in Table 3.1.
No of trajectory points 595 Spacing between trajectory points Segment 1: 2 cm
Transmitted signal Root raised cosine Channel sounder Correlation type
The agent trajectory is divided into 7 segments shown with different colors, c.f.
Fig A.3 The spacing between trajectory points was 2 cm for segments 1 and 2, and
In the experiment, the precise locations of the trajectory points were initially unknown, prompting the use of the SLAM algorithm to estimate both the trajectory positions and the locations of the virtual anchors (VAs), including the physical anchors The results of these estimations are illustrated in Figure 2.3.
For Anchor 1, there are the VAs a (1) 2 , a (1) 4 and a (1) 5 indicated by superscript index
The article discusses the single reflections related to various architectural elements, specifically the East Plaster Board (EPB), West Wall (WW), North Glass Window (NGW), and South Wall (SW) For Anchor 1, reflections are noted on the EPB, WW, and NGW, while Anchor 2 highlights reflections on the EPB, SW, and WW, indicated by the respective indices.
To estimate the expected delays τ k (p) based on the positions of transmitters and receivers, we calculate τ k (p) = 1/c ∥a k − p∥ Subsequently, the SMC amplitudes αˆ k (p) are derived from the received signals, utilizing these delays in equation (2.4) This estimation assumes that individual SMCs do not overlap, which simplifies the interference to the DMC ν k (p) Overlapping SMCs are excluded from our dataset if the delay difference |τ k (p)−τ l (p)| is less than or equal to T 2 p for k ≠ l Ultimately, we normalize the SMC amplitudes to eliminate distance dependence, resulting in normalized amplitude data ψ(ϕ k (p)) and phase data ζ(ϕ k (p)), as defined in equations (3.3) and (3.4) The trajectory and VA positions are then aligned with the direction angles ϕ k (p) ∠(p−a k ) for GPR applications.
The datasets, denoted as D k ={ϕ k (p), y k (p)}p∈P, consist of direction angles ϕ k (p) and corresponding data points y k (p), which can represent either absolute values ψ(ϕ k ) or phases ζ(ϕ k ) The index k differentiates between various SMCs and two anchors For Anchor 1, we examine datasets related to the Line of Sight (LOS), the Extended Path Block (EPB), and the Next Generation Wave (NGW), while for Anchor 2, our focus is on the EPB and the Spatial Wave (SW).
The GP model is developed using the Matlab function fitrgp (version R2018a), and predictions are generated with the predict function We will analyze the regression results to determine the feasibility of employing GP regression for modeling SMC amplitudes Additionally, the performance of GPR will be quantitatively assessed through the SMSE and MSLL metrics in Section 3.4.4.
Table 3.2 presents the learned hyperparameters θ k abs (or θ ph k ) derived from measurements, revealing that the characteristic correlation angle of the Line of Sight (LOS) GP amplitude exhibits the highest angle correlation, indicating minimal variation across a wide angle range This stability may stem from two factors: the minimal impact of DMC on LOS amplitudes, as evidenced by the low DMC standard deviation σ abs ν,k, and the fact that estimated LOS amplitudes rely solely on the antenna pattern A(ϕ k (p)), with the reflection coefficient Γ1(ϕ1(p)) set to one In contrast, the characteristic correlation angles of the Scattered Multi-Path (SMC) GP amplitudes are notably smaller, suggesting a greater variation in estimated SMC amplitudes over angles This variation indicates an angle-dependent reflection coefficient Γ k (ϕ k (p)) and a more significant influence of DMC, corroborated by the higher DMC standard deviation σ abs ν,k These findings are further illustrated in the subsequent figures, and all estimated and modeled SMC amplitudes are normalized as defined in Eq 3.3.
Figure 3.1 presents the regression results for the LOS amplitude linked to Anchor 1, along with several SMCs related to Anchors 1 and 2 The visual representation highlights the estimated SMC amplitudes, indicated by colored markers, for each individual segment, as well as the preceding data.
Table 3.2: Parameters of the GP model for the absolute value of the SMC amplitudes.
The article discusses the characteristics of various metrics related to mean and standard deviation in the context of DMC, focusing on the correlation angle and GP standard deviation Key variables include the absolute mean (m abs), phase mean (m ph), standard deviation (σ ν,k), and correlation parameters (a abs, a ph) The analysis covers both linear and radian measurements, emphasizing the importance of these metrics in understanding data distributions and relationships.
The analysis of NGW reveals a predicted mean of 3.79 and a standard deviation of 0.826, illustrated in relation to the angle of departure ϕ2(p) The expected values are depicted with a red solid line for the mean and black dashed and blue dash-dotted lines for the standard deviation Additionally, the ±2σ range indicates the upper and lower limits that encompass 95% of the data points, highlighting the variability in the results.
Figure 3.1a illustrates the LOS amplitudes, revealing that the predicted mean value of the LOS GP amplitude exhibits minimal variation with the angle ϕ1(p), as dictated by the antenna pattern A(ϕ1(p)) Additionally, the predicted standard deviation remains low due to the significant learned DMC standard deviation and the substantial correlation angle characteristic.
The predicted mean values of the SMC GP amplitudes exhibit significant variations with the angle ϕ k (p), as illustrated in Figures 3.1b-3.1e These variations are primarily driven by the angle-dependent reflection coefficient Γ k (ϕ k (p)), while the antenna pattern A(ϕ k (p)) shows a slower variation across the entire observation angle.
The predicted standard deviation is significantly larger than that of the LOS amplitude, as detailed in Section 3.5.3 The impact of varying reflection coefficients from different building materials is evident for the SW (at a (2) 3) and the NGW (at a (1) 5), as illustrated in Figures 3.1d and 3.1e In Figure 3.1d, sections A∗, C∗, and B∗ represent the whiteboard, metal door, and a small plasterboard area, respectively Notably, for angles between -260 to -230 degrees, fluctuations are minimal due to strong reflections from the metallic whiteboard.
At angles exceeding -230 degrees, the amplitude experiences significant fluctuations as the point of reflection shifts to sections B* and C*, which consist of different materials Additionally, the variance among data points increases, particularly for positions farther from the VA a (2) 3, influenced by a stronger impact of the DMC and the longer travel distance needed to normalize the SMC amplitude This phenomenon is illustrated in Figure 3.1e, where the amplitude variations caused by differing reflection materials are evident.
(e) seg 1 seg 2 seg 3 seg 4 seg 5 seg 6 seg 7 GPR mean − 2σ +2σ
Chapter conclusions
This chapter introduces a propagation model for SMC, enabling the analysis and prediction of SMC amplitude across an entire floor plan with minimal measurements Utilizing Gaussian Process Regression (GPR), the model learns the Gaussian Process Model (GPM) to forecast SMC amplitude at new locations The chapter details the GPR model, the prediction process, and the quality of the predictions, referencing data from measurement campaign 2 found in Appendix A.2.
The study demonstrated that the proposed propagation model is effective for indoor UWB environments, with the predicted means and variances from Gaussian Process Regression (GPR) aligning closely with measured data These predictions can be utilized to calculate Signal-to-Interference-plus-Noise Ratio (SINR) and other performance metrics, as detailed in the following chapter.
RADIO ENVIRONMENT MAP FOR SITE-SPECIFIC
Related work
The quality of communication links in mobile wireless networks fluctuates with each transmission, influenced by the mobility of communication terminals and their dynamic environments As terminals move, their changing positions lead to variations in propagation losses, while also affecting the interference levels experienced by receivers Additionally, interference can vary even when terminals remain stationary.
An effective transmission system design often prioritizes performance under the worst channel conditions to ensure reliable communication However, this approach can lead to inefficient energy use and prolonged transmission times during favorable conditions By implementing a well-designed adaptive transmission protocol, it is possible to maintain reliable communication even in challenging environments while optimizing energy consumption and reducing transmission duration when channel conditions improve.
MIMO technology is recognized as a key solution for meeting the high data rate requirements of future wireless networks by enhancing spectral efficiency and improving link reliability Upcoming systems are anticipated to optimize performance by dynamically adapting to changing propagation conditions, including adjustments to parameters that cater to varying channel characteristics such as the channel state matrix, signal-to-noise ratio (SNR), and interference levels.
A system can be either open or closed-loop, i.e without or with CSI feedback.
System adaptation utilizing Channel State Information (CSI) feedback tends to enhance performance, but this improvement often incurs higher hardware costs and increased CSI feedback rates, making it sensitive to feedback delays Such delays can result in outdated channel information at the transmitter, which complicates decisions related to transmit antenna selection and adjustments in transmission rate or power, ultimately leading to a deterioration in symbol error probability (SEP) and bit error rate (BER).
It is, of course, more significant in fast-fading channels, where a return link delay might render any channel information completely outdated by the time the adaptation actually takes place.
Channel prediction based on CSI from feedback has been investigated thoroughly.
Kalman filtering and adaptive channel estimation techniques are commonly utilized to estimate one coefficient at a time A novel adaptive long-range prediction (LRP) method for flat fading channels has been introduced, enabling the estimation of an entire block of future coefficients, which allows for the prediction of future deep fades and fading variations This method utilizes an autoregressive (AR) model to represent the fading channel and calculates the minimum mean-square-error (MMSE) estimate for future fading coefficients based on previous observations Additionally, the concept of long-range channel prediction has been adapted for frequency-selective multipath fading in frequency-hopping channels with coherent detection.
In this thesis, we aim to predict channels using a database of pre-collected measurements rather than relying on CSI feedback Unlike previous methods that incorporate time-stamped data, our approach utilizes location-based data, akin to crowd sensing techniques Crowd sensing is an efficient, zero-effort method for automatically gathering and processing data, leveraging numerous agents that traverse an environment and periodically or on-demand transmit their sensory data and locations to the database.
A transmitter antenna selection scheme utilizing maximal-ratio combining (MRC) at the receiver has been analyzed, focusing on selecting the optimal antenna for transmission based on fading statistics The study derives the TASP/MRC symbol error probability (SEP), outage probability, and fading statistics by first determining the probability density function (pdf) of the maximum signal-to-noise ratio (SNR), denoted as fγ max (γ) This pdf characterizes the distribution of the random variable γmax, representing the best SNR among all paths.
This thesis focuses on predicting channel gains and SINRs for a specific site, taking into account particular positions of power amplifiers (PAs) and vertical antennas (VAs), along with their visibility and corresponding reflection coefficients While the predictions are primarily limited to small cells (SMCs), they can also be adapted for deployment in dense microcells (DMs).
In a MIMO system, techniques like TAS/MRC or beamforming can be utilized to target a dominant path, specifically through SMC By analyzing the predicted SINR or the amplitude of individual SMC, one can estimate the total SINR or received power Consequently, this allows for the forecasting of additional performance metrics, including SEP and outage probability.
In this chapter, we will demonstrate how to predict the amplitude, Signal-to-Interference-plus-Noise Ratio (SINR) of individual Spatial Modulation Channels (SMCs), and the Peak Energy Budget (PEB) across a large-scale area, specifically throughout the entire floorplan.
Radio environment map (REM) using Gaussian Process regression (GPR) 47 4.3 SMC amplitudes
To construct a REM for the PEB, a spatial field model for SMC amplitudes and dense multipath interference power is essential A Gaussian-process model (GPM) is utilized to learn the amplitude model from observed data, as detailed in chapter 3 During the training phase, SMC amplitudes can be estimated from the channel impulse response (CIR) By knowing the positions of the virtual agent (VA) and the agent, expected delays can be deduced, leading to the calculation of the estimated amplitudes.
Finally, the distance dependence will be removed from the SMC amplitudes, yielding the normalized amplitude data γ k (p) = ˆα k (p) ∥ a k −p ∥ exp
The antenna pattern and reflectivity of the reflecting surface are assumed to depend solely on the direction angle ϕ k (p) =∠(a k−p) This direction dependence is effectively modeled using Gaussian process regression Multiple datasets are collected, denoted as D k = {ϕ k (p), γ k (p)} for p∈P, ensuring that only non-overlapping SMCs are utilized in the analysis.
Using the data sets and hyper-parameters θ abs k of the GPM, one can estimate the mean E[ψ(ϕ k(p ∗ ))|D k ,θ abs k ] and variance V[ψ(ϕ k(p ∗ ))|D k ,θ k abs ] of the normalized SMC amplitudes at any desired agent position p ∗ This allows for the calculation of the SINRk(p ∗ ) and the PEB P(p ∗ ), which are the focus of the REMs discussed in this paper.
2V[ψ(ϕ k(p ∗ ))|Dk,θ k abs ], (4.2) c.f B Note that the predictedSIN R k (p ∗ )is independent of the anchor-agent distance
Section 4.3, 4.4, 4.5 shows how the spatial fields are learnt Section 5.2 and 5.4 show how these information are utilized for the single-anchor multipath-based localization algorithm.
Figures 4.1 show the GPR implementation on various SMC amplitudes It is shown that there is a correlation between the SMC amplitude and its corresponding angle.
The Signal-to-Interference-plus-Noise Ratio (SINR) for reflections on the EPB is significantly high, reaching approximately 40, as illustrated in Figure 4.1b, which surpasses the SINR levels of other SMCs shown in Figures 4.1c to 4.1n, with the exception of the Line of Sight (LOS) link It is important to note that the east side of the room has minimal obstacles that may enhance link quality; however, the combination of a flat reflecting surface and high-quality materials provides a plausible explanation for this elevated SINR.
SINR segment 1 segment 2 segment 3 segment 4 segment 5 segment 6 segment 7 GPR mean GPR mean + 2std GPR mean - 2std GPR SINR
Figure 4.1 illustrates Gaussian Process (GP) regression applied to SMC amplitudes across various scenarios: (a) Line of Sight (LOS) link, (b) reflection from the EPB, (c) reflection from the WW, (d) reflection in the southern section of the room with diverse materials such as a whiteboard, wall, and metal door, (e) reflection in the northern section featuring glass windows and walls, and (f) double reflection involving the EPB followed by the WW.
Figure 4.1: GP regression on SMC amplitudes corresponding to: (g) double reflection on EPB then
The process involves a series of double reflections, starting with SW followed by EPB, then transitioning to NGW Next, the sequence continues with double reflections on WW leading to EPB, followed by reflections on WW resulting in SW The method also includes double reflections on SW that culminate in GW, and finally, double reflections on SW that revert to WW.
Figure 4.1: GP regression on SMC amplitudes corresponding to: (m) double reflection on NGW then
SW, and ( n ) double reflection on NGW then WW The regressed amplitude is | α k (p)d k (p) | SINR resulted from GPR is plotted in green with axis on the RHS.
The reflections on the west wall show a low Signal-to-Interference-plus-Noise Ratio (SINR), indicating poor link quality, except in a direction nearly perpendicular to the wall where SINR improves significantly This observation is logical, as the presence of various obstacles such as computers and measuring equipment near the west wall contributes to scattering effects that degrade the signal quality.
In the analysis of SMC corresponding to VA 4, it is evident that reflections on the whiteboard exhibit a significantly higher Signal-to-Interference-plus-Noise Ratio (SINR) compared to those on other materials such as metal doors and walls Additionally, for VA 6, reflections on glass windows demonstrate a commendable link quality with an SINR of approximately 20.
Figures 4.1f, 4.1g, 4.1i, and 4.1k illustrate that for VA 7, 8, 11, and 13, the link quality is superior to other second-order SMCs but falls short compared to first-order SMCs, as demonstrated in Figures 4.1h, 4.1j, 4.1l, 4.1m, and 4.1n.
SINR
In this thesis, we introduce a method for predicting the Signal-to-Interference-plus-Noise Ratio (SINR) of the k-th Small Cell (SMC) based on varying locations, denoted as SINR k (p) This approach aims to improve the performance of tracking filters referenced in [49] and has additional applications discussed in section 4.5.
Implementing GPR on measurement data enables the prediction of SINR and the amplitude of various SMCs, highlighting that the LOS link demonstrates significantly higher SINR, making it a reliable choice In scenarios where LOS is unavailable, selecting an optimal NLOS link for antenna direction becomes crucial This approach relies on two key parameters: SINR and SMC amplitude Notably, reflections from surfaces like whiteboards yield links with high power but low SINR, as illustrated in the accompanying figures.
The predicted SMC amplitude α k (p) across the entire floor plan is illustrated in Figure 4.2, showcasing various link scenarios: (a) line-of-sight (LOS), (b) reflection from the east partition board (EPB), (c) reflection from the west wall (WW), (d) reflection from the southern section of the room, (e) reflection from the northern section of the room, and (f) double reflection first from the EPB and then from the WW.
The predicted SMC amplitude α k (p) for the entire floor plan demonstrates various link scenarios, including double reflections off the west wall (WW) followed by the east perimeter boundary (EPB) and double reflections from the south wall to the glass window (GW) Utilizing Ground Penetrating Radar (GPR) along the measurement trajectory reveals that glass windows enhance link quality, particularly in high-rise buildings where larger windows are common Consequently, it is advisable to consider the SMC corresponding to VA 6 for optimal performance, as double reflections also yield strong and reliable links.
Figure 4.2 illustrates that the Line of Sight (LOS) amplitude is primarily influenced by distance rather than the antenna's radiation pattern In contrast, other Surface Mount Components (SMCs) demonstrate that their amplitudes are significantly affected by reflection coefficients.
Position error bound
A directional, multipath-resolved radio environment map was proposed based on a simplified Path Loss Environment Block (PEB) in [87] This PEB serves as a metric for selecting directional antennas in the single-anchor localization multipath-assisted algorithm (SALMA) However, the PEB is calculated per reflector from the Spatially-Multiplexed Channel (SMC) Signal-to-Interference-plus-Noise Ratio (SINR) This thesis enhances the approach by utilizing Gaussian Process Regression (GPR) to predict the SINR for individual SMCs at specific locations, resulting in a higher resolution PEB Radio Environment Map (REM).
Figure 4.4 illustrates the predicted PEB across the floor plan, highlighting the significant contributions of various VAs to the localization algorithm Notably, VAs 2, 4, 6, 7, and 8 play essential roles in enhancing the PEB.
Because there are straight lines indicating lower PEB originating from these VAs in the sub-figures.
Second-order virtual anchors (VAs) play a crucial role in localization algorithms, significantly enhancing Positioning Error Bound (PEB) even in the absence of a Line of Sight (LOS) component In contrast, relying solely on first-order VAs leads to poorer PEB outcomes.
The predicted Signal-to-Interference-plus-Noise Ratio (SINR) for the entire floor plan is illustrated in Figure 4.3, showcasing various link scenarios: (a) Line of Sight (LOS), (b) reflection on the External Partition Wall (EPB), (c) reflection on the Window Wall (WW), (d) reflection in the southern section of the room, (e) reflection in the northern section of the room, and (f) double reflection involving both the EPB and WW.
Figure 4.3: ( g ) double reflection on WW then EPB, ( h ) double reflection on EPB then NGW, ( i ) double reflection on WW then EPB, ( j ) double reflection on WW then SW, ( k ) double reflection on
SW then GW, (l) double reflection on SW then WW
The predicted Signal-to-Interference-plus-Noise Ratio (SINR) across the entire floor plan varies based on different link scenarios, specifically double reflections on NGW followed by SW and WW This SINR data is derived from Gaussian Process Regression (GPR) applied to Channel Impulse Responses (CIRs), measured at 595 points along the designated trajectory, as illustrated in Figure A.3, using a consistent dB scale.
Chapter conclusions
In this chapter, GPM developed in Chapter 3 is used to predict certain performance indicators throughout the whole floor plan, which are SINR, SMC amplitudes, PEB.
It is shown that using GPM, large-scale statistics of CQM can be predicted.
PEB using all VAs and PA
PEB using 1st order VAs and PA
PEB using 1st order VAs
PEB using selected VAs and PA
Figure 4.4 illustrates the predicted PEB from GP, utilizing data from SMCs across various configurations: (a) incorporating all VAs along with the physical anchor, (b) including all first and second order VAs, (c) focusing on first order VAs together with the physical anchor, (d) analyzing solely first order VAs, (e) examining selected VAs and LOS, and (f) evaluating only selected VAs.
APPLICATION OF GPR - ENABLED REMS TO ROBUST
Related work
The Internet of Things (IoT) vision encompasses diverse applications across various domains, including industrial sectors, healthcare, smart cities, and mobility solutions Concurrently, the development of 5G and future wireless networks aims to achieve ultra-low latency, high user densities, and exceptional data rates to support a wide range of end-user scenarios Location information plays a vital role in these applications, enhancing context-awareness and meeting varying service quality requirements In particular, for assisted and autonomous driving, precise location data is critical, necessitating 100% availability for high-end location-based services Additionally, the discussions surrounding robustness, security, and privacy in IoT applications highlight the importance of high-accuracy location information as a fundamental enabler for location-based services within IoT and 5G networks.
Significant advancements have been made in accurate and robust position estimation, highlighting the diverse scenarios and applications involved RSS-based techniques are particularly effective for positioning using signals-of-opportunity, as they eliminate the need for dedicated time stamping and synchronization By utilizing RSS measurements, positions can be determined through various methods, including path-loss based range estimates, ray-tracing propagation predictions, fingerprinting and machine learning techniques, and device-free tomography-inspired measurements However, the primary drawback of RSS-based approaches is their lower accuracy and robustness compared to other measurement principles, especially in the presence of multipath fading and shadowing.
Time-of-Flight (ToF) measurements and multilateration form the foundation of high-accuracy positioning systems, such as Global Navigation Satellite Systems (GNSS) The variance in ToF ranging errors inversely correlates with the squared bandwidth and Signal-to-Noise Ratio (SNR), highlighting the benefits of utilizing high signal bandwidth While SNR is only slightly affected by range—thanks to power control mechanisms in the network—multipath effects can significantly impact positioning accuracy These principles are essential for analyzing the positioning performance of wireless networks.
[64, 111], showing the influence of the geometry (and number) of the nodes that are being involved in the position computation.
The availability of sufficiently accurate location information is a facilitator for ex- ploiting “location awareness” to enhance the performance of the radio access network
Location-awareness enhances wireless communication systems by utilizing geometric information to optimize algorithms and protocols across various layers of the protocol stack, aiming for improved throughput, reduced latency, and increased robustness At the upper layers, location data is directly applied in routing algorithms, while at the lower layers, a Channel Quality Map (CQM) is utilized to correlate network performance indicators, such as channel capacity or Signal-to-Interference-plus-Noise Ratio (SINR), with specific locations, resulting in the creation of a "radio environment map."
The REM is derived from a pre-existing database created through prior measurements To enhance data collection over extensive spatial areas, crowd-sensing methods utilize numerous agents navigating the environment To manage this large database and facilitate accurate predictions, a regression tool is essential Gaussian Process Regression (GPR) is particularly valuable as it allows for the creation of inference algorithms with complexity that remains consistent, regardless of the number of observations.
Situational awareness involves collecting location information of radio nodes alongside details about the propagation environment, which includes SMCs, their AOAs, AODs, corresponding delays, and reflection points This data can be extracted from channel measurements using a SLAM algorithm, where SMCs are represented as VAs, or mirror images of anchors relative to various reflecting surfaces By integrating VA positions with a data association algorithm, multipath-assisted, single-anchor localization and tracking algorithms can be developed, achieving centimeter-level accuracy with UWB signals The crowd-sourcing of such environmental map information has been explored, and situational awareness is particularly crucial for beam prediction in mmWave radio systems.
This chapter integrates a VA-based geometric environment model with a GPR model to enhance single-anchor localization algorithms The VA model predicts delay, Angle of Arrival (AOA), and Angle of Departure (AOD) of SMCs, while the GPR model forecasts their amplitudes, as detailed in [J1] We demonstrate how the REM significantly improves the robustness of localization in multipath environments.
Problem formulation
Equation (2.3) can be rewritten as r=S(p)α+w ∼ CN(S(p)α,C), (5.1) wherer = [ , r(nTs), ],S(p) = [ ,s(τk(p)), ]; ands(τ) = [ , s(nTs−τ), ] T ∈
C N denotes the SMCs with delaysτ k (p)that are determined byp,α= [ , α k , ] T ∈
In this article, we discuss the SMC amplitudes represented by C and K, where C = E[ww^H] signifies the covariance of the noise vector w, applicable for both AWGN and DMC scenarios We explore the maximum likelihood (ML) estimation method, expressed as pˆ = arg max p ∗ L(r|p ∗), which treats α as nuisance parameters and aims to determine the optimal position by maximizing the concentrated log-likelihood function (LLHF).
The LLHF evaluated at candidate positionp ∗ :
L(r|p ∗ ,α) =−log det(C)−(r−S(p)α) H C −1 (r−S(p)α) (5.3) followed from (5.1) The maximization in (5.2) is solved by weighted least square solution for∥r−S(p)α∥ 2 which yieldsαˆ = S H (p)C −1 S(p)−1
ML positioning algorithm is our inherent algorithm, abbreviated as "SALMA-light" in
The GPM model offers prior knowledge regarding the absolute value of α, but it does not provide information about its phase To address this, we expand the amplitude vector as α = Φx, where Φ is a diagonal matrix defined as Φ = diag(ϕ) with [ϕ]k = exp(j∠α k) = exp(jφ k) According to the GPM, the variable x conditional on p follows a normal distribution, denoted as x|p ∼ N à(p), 1 2 Λ(p), where [à(p)]k represents the expected value E { ψ(ϕ k (p))|D k ,θ abs k }.
∥a k −p∥ , and the diagonal matrix has elements[Λ(p)] k,k = 2 V { ψ(ϕ k (p))|D k ,θ abs k }
∥a k −p∥ 2 The problem becomes: pˆ= arg max p ∗ L(r|p ∗ ,α) s.t x|p ∗ ∼ N à(p ∗ ),1
Proposed algorithm
The signal model then becomes r=S(p)Φà(p) +S(p) ˜x+w (5.5) withx˜|p∼ CN(0,Λ(p)) is introduced to account for the variance of the SMC ampli- tudes and the uncertainty of the phases inΦ.
The concentrated LHF is now obtained by maximizing the LHF for signal model (5.5) by concentrating out the nuisane parameter vectorΦand σ n 2 (maximizing the AWGN model forC) given candidate position p ∗
L(r|σn,ϕ,p ∗ ) =−log det( ˜C)−(r−S(p)M(p)ϕ) H C˜ −1 (r−S(p)M(p)ϕ) (5.7) whereM(p) = diag(à(p))and
First, we will find the phase ϕ, and noise varianceσ n 2 that maximize (5.7), i.e. ϕˆ = arg max ϕ L(r|σ n ,ϕ,p ∗ ) (5.9) ˆ σ n = arg max σ n L r|σ 2 n ,ϕ,ˆ p ∗
Let’s denote the phase of the k-th SMC amplitude as φ k To solve for the phase, we have:
Vector rk is the residual of the CIR measurement after subtracting all SMCs except the k-th.
In order to find φ k , let’s denotee jφ k =a k +jb k Thus: ˆ a k ,ˆb k = arg min a k ,b k f(a k , b k ) s.t g(a k , b k ) =a 2 k +b 2 k −1 = 0 (5.12) Using Lagrange multiplier, we have ˆ a k ,ˆb k ,λˆ k = arg min a k ,b k ,λ k f(a k , b k ) +λ k g(a k , b k ) (5.13) and obtain
Equating equations (5.14), (5.15), and (5.16) to zero yields key relationships for λ k and a k, expressed as λ k = |s H (τ k ) ˜C −1 à k rk| − à 2 k s(τk) H C˜ −1 s(τk) and a k = s(τk) H C˜ −1 à k ℜ{rk} à 2 k s(τk) H C˜ −1 s(τk) + λ k, respectively For b k, similar expressions apply In summary, φ k is represented as φ k = ∠s(τ k) H C˜ −1 à k rk, and if the k-th SMC is non-overlapping with others, it simplifies to ˆ φ k = ∠s(τ k) ˜C −1 r, indicating a weighted projection of the measurement onto the k-th SMC template s(τk) The weighting by C˜ −1 accounts for the variance from the GPR model, which is crucial for minimizing secondary maxima in the LHF; however, this weighting adversely affects the reliability of the phase estimation process.
We thus replace for this estimator the covariance by an identity matrix, obtaining the approximate (but more robust) phase estimator ˆ φ k ≈∠s (τ k ) r (5.21)
(5.22) whereCˆ˜ = (r−S(p)M(p)ϕ) (r−S(p)M(p)ϕ) H is a realization ofC˜ According to
Thusσˆ n can be computed The localization problem reduces to: pˆ = arg max p ∗ L r|σˆn,ϕ,ˆ p ∗
Result
To implement the GPR-based positioning algorithm, the data is divided into two groups: one for GP training, where both agent positions and corresponding CIRs are known, allowing for the estimation of GPM hyper-parameters, and another group where only CIRs are used, with unknown agent positions estimated through the REM, leveraging SMC amplitudes and SINRs predicted by the GPM hyper-parameters The errors from this process are computed, and their cumulative distribution functions (CDFs) are illustrated in Figure 5.1 For comparative analysis, the single-anchor localization method SALMA-light is utilized.
Figure 5.1: CDF of the localization error using ( a ) training segments 1, 2, 3, 7, ( b ) training segments
The blue solid line represents the error cumulative distribution function (CDF) achieved with SALMA-light, while the orange solid line illustrates the error CDF obtained by optimizing the LLHF using prior knowledge from Gaussian Process Regression (GPR).
The phase φ k is approximated by using the phase from CIR Please note that, overlap checking is performed first before implementing the algorithms.
It is shown that, using the situational awareness through the REM information, the proposed algorithm outperforms SALMA-light in terms of the outlier robustness, while the accuracy remains comparable.
Figure 5.2 illustrates the performance enhancement by comparing the LLHF of two algorithms The LLHF was assessed at candidate positions based on the estimated line-of-sight distance The results indicate that the REM-assisted algorithm effectively decreases the number of local maxima in the LLHF, highlighting the correct maximum and resulting in improved performance compared to SALMA-light.
In a modified experiment illustrated in Figure 5.3, an error CDF demonstrates that implementing a visibility test and overlap checking effectively minimizes the number of SMCs utilized for position estimation to the most relevant ones for both SALMA-light and the proposed algorithm The results indicate that the proposed algorithm significantly outperforms SALMA-light in reducing outliers The contrast between the findings in Figure 5.1 and Figure 5.3 arises from the reduction of VAs after the visibility test and overlap checking, which compromises the robustness of SALMA-light, while the proposed REM method maintains robustness without such a loss Additionally, this variant shows an improvement in accuracy.
The proposed algorithm shows potential for improved performance in obstructed line-of-sight (LOS) scenarios, even without specific adaptations for such conditions Recent studies highlight algorithms that enhance robustness against blocked LOS and sensor measurements caused by human presence and obstacles Notably, the belief propagation SLAM algorithm is referenced as a significant approach in addressing these challenges.
[52] provides visibility information of SMCs in addition to the amplitude and delay information This visibility information can be used to pre-select the data points for
Evaluation points Estimation result True position
LHF+GPR approximate phase exact sigma
Evaluation points Estimation result True position
Figure 5.2 illustrates the LLHF values derived from (a) SALMA-light and (b) LHF+GPR with precise sigma, showcasing evaluation points color-coded for clarity The red circle indicates the estimation result, while the filled black circle marks the true position The development of a GPR-based Radio Environment Map (REM) aims to ensure that path blocking does not compromise the REM's quality It is anticipated that a well-learned REM, based on extensive independent measurements from various user equipment, will effectively distinguish between the "environment part" of the propagation channel and the "device part." A detailed formulation of these methodologies is planned for future research.
Figure 5.3: CDF of the localization error using ( a ) training segments 1, 2, 3, 7, ( b ) training segments
The blue solid line illustrates the error cumulative distribution function (CDF) achieved with SALMA-light, while the orange solid line represents the error CDF obtained by optimizing the LLHF using prior knowledge derived from Gaussian Process Regression (GPR).
The phase ζ k is approximated by using the phase from CIR Visibility test is carried out, followed by overlap checking, before implementing the algorithms.
Chapter conclusions
This chapter illustrates how CQM enhances the robustness of localization algorithms By utilizing predicted SMC amplitudes and their corresponding variances, a single-anchor multipath-assisted localization algorithm becomes more resilient to obstacles.
Recent advancements in positioning technologies, achieving sub-meter to centimeter accuracy, are set to enhance location information in 5G and beyond-5G devices This improved data will facilitate quicker antenna lock-on in mmWave beamforming and enable the adaptation of communication protocols to boost efficiency These innovations are integral to the development of location-aware communication systems.
Location-aware communication systems face significant challenges, primarily in achieving location awareness and spatial channel modeling Location awareness involves seamless localization, including handover, technology integration, and error management in harsh environments Meanwhile, spatial channel modeling requires addressing position uncertainties, the non-stationary nature of channel statistics, and adopting a structured approach for database prediction and maintenance.
This dissertation deals with these two challenges.
This dissertation introduces a location-aware communication system utilizing a multipath-based channel model that focuses solely on resolved specular multipath components (SMCs) This method offers several benefits, including its compatibility with Ultra-Wideband (UWB) and millimeter-wave (mmWave) MIMO systems Each SMC is linked to a virtual antenna (VA), providing valuable location-related information Furthermore, when combined with the MINT algorithm for positioning and tracking RF devices and the SLAM algorithm for environmental mapping, the construction of the CQM database becomes significantly more autonomous.
This dissertation presents three significant contributions, addressing three key research questions and hypotheses Firstly, it introduces a site-specific propagation model, providing a structured approach to predicting and learning Channel Quality Maps (CQMs) Additionally, it proposes a method for predicting radio channel statistics on a large scale, offering a fast and simple solution that reduces overhead and latency Furthermore, the dissertation demonstrates the effectiveness of CQMs in robust single-anchor multipath-based localization, even in challenging environments with blocked propagation, thereby enabling accurate positioning.
Chapter 2 of the dissertation discusses the foundational concepts of environment and system models relevant to communication scenarios involving radio signals between a mobile agent and a static base station It builds on previous research by incorporating Variational Approximation (VA) and probabilistic VA methods, which have proven effective for positioning, tracking, and environmental mapping Additionally, the chapter adapts VA/Sequential Monte Carlo (SMC)-based models for channels, signals, and systems to address specific challenges Key channel quality metrics, including SMC amplitude, Signal-to-Interference-plus-Noise Ratio (SINR), and Position Error Bound (PEB), are referenced from existing studies, while channel capacity formulations are also provided The discussion highlights the SMCs' ability to capture significant channel energy and capacity, supporting the efficacy of the SMC-based approach for location-aware communication systems.
Chapter 3 presents the radio propagation model for individual SMC [C3,J1] GPR [C2,C3,J1] is used to analyze and predict SMCs’ amplitudes and phases Measurement data from campaign 2 is used to evaluate the regressor’s quality [J1] It is shown that the method is more accurate in predicting power of individual link, compared to a state-of-the-art machine learning regressor for a mmWave beamforming application.
In Chapter 4, Gaussian Processes (GP) are utilized to forecast the REM of channel qualities in different environments, enhancing location-aware applications The study demonstrates that Signal-to-Interference-plus-Noise Ratio (SINR) and Path Error Bit (PEB) can be predicted easily, potentially reducing overhead and latency.
In Chapter 5, the SMC amplitudes derived from Chapter 4 are utilized as supplementary information to enhance the robustness of single-anchor multipath-based localization, particularly in scenarios involving human or object obstruction This finding is consistent with previous research.
In the future, we aim to explore the integration of Ground Penetrating Radar (GPR) with Radio Environment Maps (REMs) in wireless communication systems, particularly those utilizing wide-bandwidth technologies like DS-CDMA By leveraging REM data, we can develop an adaptive communication protocol that optimizes resource utilization effectively.
We also would like to demonstrate the usefulness of REM for a single-anchor local- ization system when there are human blocking or obstacles.
In their 2016 study, Hong-Anh Nguyen and colleagues conducted a comprehensive channel capacity analysis of indoor environments specifically for location-aware communications Presented at the IEEE GLOBECOM Workshops in Washington DC, this research explores the factors influencing communication efficacy in indoor settings, providing valuable insights for enhancing wireless connectivity and location-based services The findings, documented in the proceedings (ISBN: 978-1-5090-2482-7, pp 1-6), contribute significantly to the field of wireless communication and its applications in indoor environments.
In their 2017 paper presented at the International Conference on Recent Advances in Signal Processing, Telecommunications and Computing (SigTelCom) in Da Nang, Vietnam, Hong-Anh Nguyen, Khanh-Hung Nguyen, and Van-Khang Nguyen explored the prediction of received signal strength using Gaussian processes Their research, documented in the proceedings (ISBN: 978-1-5090-2291-5, pp 95-97), contributes valuable insights into signal processing methodologies.
In their 2018 paper presented at the 7th International Conference on Communications and Electronics (ICCE) in Hue, Vietnam, Hong-Anh Nguyen and colleagues, including Michael Rath, Josef Kulmer, Stefan Grebien, Van-Khang Nguyen, and Klaus Witrisal, explore Gaussian Process Modeling of Ultra-Wideband (UWB) multipath components This research, documented in IEEE proceedings (ISBN: 978-1-5386-3679-4, pp 291-296), contributes valuable insights into the modeling techniques for UWB communications, enhancing understanding of multipath effects in wireless systems.
4 [J1]Hong-Anh Nguyen, Michael Rath, Erik Leitinger, Van-Khang Nguyen, and Klaus Witrisal (2020),Gaussian Process Modeling of Specular Multipath Compo- nents, Applied Sciences, DOI: 10.3390/app10155216, (ISI Q1), 2020.
5 [J2] Hong-Anh Nguyen, Van-Khang Nguyen, and Klaus Witrisal, AmplitudeModeling of Specular Multipath Components for Robust Indoor Localization, Sen- sors, DOI: 10.3390/s22020462,(ISI Q2), 2022.
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Description of channel measurement campaigns
Frequency Domain Measurements - Vector Network Analyzer
Frequency-domain measurements have been obtained with a Rhode & Schwarz ZVA-
The 24 VNA operates within the full FCC bandwidth of 3.1 to 10.6 GHz, translating to a wavelength range of 9.67 cm to 2.83 cm, which enables a delay resolution of 0.1333 ns and a spatial resolution of 4 cm At each trajectory position, a sampled version H l [k] of the CTF H l (f) is obtained with a frequency spacing of ∆f The VNA undergoes calibration up to the antennas using a through-open-short-match (TOSM) method Measurements across the FCC bandwidth are conducted at various discrete frequencies, achieving a frequency resolution of 1.5 MHz, while the transmit power is maintained at 15 dBm.
In VNA measurements, the TOSM calibration has effectively eliminated major system influences on the measured CTF H(f), including cables and connectors, while antennas remain integral to the transmission channel The subsequent post-processing involves filtering the signal to isolate a specific frequency band within the FCC range and downconverting the time-domain signal to achieve a baseband signal This filtering utilizes a baseband pulse s(t) that encompasses the required bandwidth.
The CTF is evaluated at Nf discrete frequencies defined as fk = k∆f + fmin, where k ranges from 0 to Nf − 1, with fmin being the lowest frequency measured This sampled CTF, denoted as H[k], represents a Fourier series of the time-domain CIR h(τ), which is periodic with a period of τmax By identifying f0 and fc as the lower band edge and the center frequency of the extracted band, respectively, and applying an IFFT of size NFFT = ⌈(∆f∆τ) −1⌉, the time-domain equivalent baseband signal is derived as r(t) = IFFTNFFT {H[k]S[k]}e −j2π(fc − f0)t In this equation, S[k] represents the discrete frequency domain form of the pulse s(t) within the specified frequency range, following a methodology akin to previous studies.
In a straightforward scenario depicted in Fig A.1, a physical anchor is located at position a₁ = [4.2, 4] T, while a mobile agent is positioned at p = [3.4, 1.4] T UWB grid measurements were collected for 484 grid points (22x22) surrounding the agent, with a spacing of 5x5 cm These measurements utilized a Rhode & Schwarz ZVA-24 vector network analyzer operating within a frequency range of 3.1–10.6 GHz, encompassing the entire FCC-regulated UWB band Both the agent and anchor were equipped with dipole-like antennas fashioned from Euro Cent coins, mounted at a height of 1.5 m, featuring a nearly uniform radiation pattern in the azimuth plane and nulls in the vertical directions The actual signal band was selected from the total measured band through filtering with a raised cosine pulse s(t) with a roll-off factor of 0.6, applying varying two-sided bandwidths of 100 MHz, 500 MHz, and 2 GHz, all centered at a carrier frequency of fₜ = 7 GHz.
This article explores indoor environments where fixed anchors communicate with a mobile agent via radio signals The scenario depicted in Figure A.3 features two physical anchor positions, indicated as blue crosses, along with the agent's positions along a segmented trajectory and several exemplary virtual anchors (VAs) These VAs are mirror images of the physical anchor positions, created by reflections from flat surfaces like walls, and their locations are influenced by the surrounding floor plan The position of the k-th VA corresponding to the j-th physical anchor is represented as a(j)k It is important to note that this study focuses solely on horizontal signal propagation, and for simplicity, the anchor index j will be omitted in subsequent discussions.
Also, we denote Las the set of measurement points.
The laboratory room at Graz University of Technology, used for experimental validation, features two plasterboard walls and two reinforced concrete walls, depicted as black outer lines in Figure A.3 The north wall includes three glass windows, represented by thick gray lines, while the south wall contains a whiteboard and a metal door, indicated by labels A* and C* Specific labels are introduced to identify the various reflection surfaces within the room.
A278 xm ym p uwin lwall lwin rwin
In the scenario illustrated in Figure A.1, a physical anchor is positioned at point a1, while a virtual agent (VA) is located at point a2 The measurement grid, represented by a gray grid with 5 × 5 cm spacing, includes various positions denoted as pℓ The center position of this grid is marked by a red dot, which indicates the actual location of the mobile agent used in the illustration.
Blue lines depict specular reflections at wall segments.
Figure A.2: Photo of corridor scenario
The channel measurements were conducted using an Ilmsens Ultra-Wide band M-sequence device, which employs a correlative channel sounding technique This method involves transmitting a binary code sequence with favorable autocorrelation properties, allowing the receiver to recover the channel impulse response through correlation with the known code The sounder features one transmitter and two receiver ports, utilizing a 12-bit M-sequence with a sequence length of 4095 samples This configuration provides an unambiguous delay window of 589.2 ns at a clock rate of 6.95 GHz, with the M-sequence modulated onto a 6.95 GHz carrier, producing a probing signal that spans a frequency range of approximately 3.5 to 10.5 GHz.
Each of the ports was connected to a dipole coin antenna as shown in Figure A.4b.
According to [81], the coin antenna has a very wide bandwidth ranging from 3 to 9 GHz It also has with a nearly isotropic radiation pattern in the horizontal plane.
In our study, we utilized two receiver ports as anchors, positioning their antennas at fixed locations a(1)1 and a(2)1 The transmitter port was linked to a movable antenna that traversed a trajectory consisting of 595 points, as illustrated in Figure A.3, enabling us to gather an equal number of channel measurements All antennas were securely mounted on tripods at a uniform height, ensuring that only the co-polarized azimuth radiation pattern of the antenna influenced the data collected The raw measurements obtained from the receiver ports were processed using a Root Raised Cosine (RRC) filter, featuring a center frequency of 6.95 GHz, a roll-off factor of 0.5, and a specific bandwidth.
D † a (1) 1 a (1) 2 a (1) 4 a (1) 5 φ k p x-direction in meter y -direction in meter segment 1 segment 2 segment 3 segment 4 segment 5 segment 6 segment 7 phys anchor VA
The floor plan of the evaluation scenario is illustrated in Figure A.3, featuring bold black lines for walls and thick gray lines for glass windows, while other lines depict various materials It includes two blue crosses indicating physical anchors and orange circles representing virtual anchors (VAs) used in the experimental validation The agent's movement is segmented into seven distinct colored parts along its trajectory.
Capital letters (with or without mark ∗ or †) refer to sub-segments of different materials along each wall.
(a) Ilmsens UWB M-sequence sounder and Ilmsens power supply (b) Europe coin an- tenna
Figure A.4: A photo of the Ilmsens channel sounder, and a photo of the coin antenna used for transmit and receive.
1/T p = 2 GHz to obtain the received signals corresponding to the model in (2.3).
The power spectral density of AWGNN 0 is known and considered in the training and evaluation process.
Time domain measurement - M-Sequence Radar
Time-domain measurements have been obtained with an Ilmsens Ultra-Wide Band M-Sequence device [124] The measurement principle is correlative channel sounding
A binary code sequence with optimal autocorrelation properties is transmitted through the channel, allowing for effective recovery of the channel impulse response at the receiver using correlation with the known code sequence The M-sequence radar system consists of one transmitter and two receiver ports, where the mobile unit acts as the transmitter along designated measurement trajectories, while the receiver ports serve as anchors Operating in FCC mode, the M-sequence device transmits at a power of 18 dBm The 12-bit M-sequence utilized has a length of 4095 samples, and with a clock rate of 6.95 GHz, it accommodates a maximum delay of 589.2 ns.
Figure A.5 shows a block diagramm of the measurement setup using the M-Sequence radar As in the VNA measurements, the measurement system should be calibrated
The calibration setup for time domain measurements excludes the antennas, necessitating compensation for the internal transfer functions of the device and the effects of measurement cables and connectors, represented by the transfer function H sys,i(f) for the i-th RX channel Additionally, crosstalk between the TX channel and the i-th RX channel, denoted as Hcross,i(f), must also be accounted for in the analysis For simplicity, we will omit the channel index in the following discussion.
To accurately assess crosstalk, two essential measurements must be conducted Initially, the TX antenna is removed, and the TX port is terminated with a 50Ω match to measure the crosstalk signals Subsequently, the RX antennas are also unmounted, and the TX and RX cables are connected, allowing for the calculation of Hmeas(f) = Hsys(f) +
The measurement of H cross (f) is conducted using a configuration that incorporates all antennas, as illustrated in Figure A.5 This results in the equation H meas (f) = H(f)H sys (f) + H cross (f) Consequently, a calibrated version of the radio channel transfer function is derived.
To mitigate excessive noise gain, we apply thresholding to the time-domain representation of the denominator, setting samples below a specific threshold to zero The time-domain signal is derived from an inverse Fourier transformation, allowing us to compute the signal within the desired frequency range around the center frequency \( f_c \) using an appropriate baseband pulse shape \( s(t) \) This results in the expression \( r(t) = h(t) * s(t) e^{j 2\pi f_c t} e^{-j 2\pi f_c t} * \delta(t - \tau_{\text{shift}}) \) The time shift \( \tau_{\text{shift}} \) accounts for connector and antenna delays not addressed in the previous equation Connector delays can be measured with a Vector Network Analyzer (VNA), while antenna delays can be calculated based on antenna length and material propagation velocity, typically provided in data sheets This calibration process is akin to the methodology described in reference [126].
The publicly available measurements [127] contain extraction functions for Matlab,that directly deliver signals in the form of (A.3).
Variance of ν k
Here, the variance of DMC ν k (p)within one estimated SMC amplitude is derived.
To enhance readability, we exclude the agent position p The DMC of an estimated SMC amplitude is expressed as ν k Z Z s(τ −λ)ν(λ)s ∗ (τ −τ k )dτdλ (B.4), assuming the energy of the signal s(t) is normalized to one, i.e., R∞.
−∞|s(t)| 2 dt= 1 Using (B.4), the variance of the DMC of an estimated SMC amplitude
Z ˜ s(τ k −λ)˜s ∗ (τ k −λ)Sν(λ)dλ (B.5) where s(t) =˜ R s(τ)s ∗ (t−τ)dτ In the case, a large bandwidth (UWB) is assumed, (B.5) can be approximated by
|S(f)| 4 df (B.7) where S(f) is the Fourier transform of s(t) and Tp = R∞
−∞|S(f)| 4 df is the effective pulse duration.
1 Assuming a signal s(t)with block-spectrum, the effective pulse duration is given asT p =R∞
−∞|S(f)| 4 df =T s , whereT s is the Nyquist sampling time.
2 Assuming a signals(t)with non-block spectrum signal, the effective pulse duration
Tp is different from Nyquist sampling time Ts For example, a raised cosine pulse results inT p =R∞
−∞|S(f)| 4 df = 1−β β T s , where β is the roll-factor.